Emergence of the geometric contribution to the superfluid density in the inner crust of neutron stars

TL;DR

This paper investigates how the geometric contribution to superfluid density arises in the inner crust of neutron stars, emphasizing the role of band theory and the importance of corrections to quasi-particle states.

Contribution

It derives the dependence of superfluid density on pairing gap in multi-band neutron systems and highlights the necessity of including quasi-particle state corrections for accurate geometric contributions.

Findings

Geometric contribution is significant in neutron star crust superfluid density.

Corrections to quasi-particle states are essential to capture the geometric effects.

Conventional calculations neglecting these corrections miss key contributions.

Abstract

The geometric contribution to the superfluid density has been found to be of great importance in the inner crust of neutron stars. In this work we clarify how this contribution arises in the context of a band theory for neutrons. Specifically, we derive the dependence of the superfluid density on the magnitude of the pairing gap when the system has many bands cutting the Fermi energy, as it is the case for the neutrons in the inner crust. Also, in the perturbation theory framework, we find that it is essential to account for the corrections to the (Bogoliubov) quasi-particle states in order to get the geometric contribution. Accounting only for the corrections to the (Hartree-Fock) single-particle states leads to the conventional contribution only.